It looks as though you're using Custom CSS, and you've overwritten the rules for those buttons with rules that break the images.

Instead of using the whole stylesheet in Custom CSS, try adding only those rules you want to change.

If you need to use the whole stylesheet, you'll want to update any references to background images with the full URL to the image. Currently the social media buttons are pointing to url(images/someimage.png) but should be url(http://pbyha.wordpress.com/wp-content/themes/pub/splendio/images/someimage.png)

Also check the "Don't use Splendio's CSS, and replace everything with my own CSS" option under CSS Settings.